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Algebraic Entropy of Elementary Amenable Groups |
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| Authors: | D V Osin |
| Institution: | (1) Department of Mathematics, SC 1326, Vanderbilt University, Nashville, TN 37240, U.S.A. |
| Abstract: | We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups. |
| Keywords: | finitely generated group growth function exponential growth rate clementary amenable group topological entropy of geodesic flows |
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